Lie group analysis for the effect of temperature-dependent fluid viscosity and thermophoresis particle deposition on free convective heat and mass transfer under variable stream conditions

This paper examines a steady two-dimensional flow of incompressible fluid over a vertical stretching sheet. The fluid viscosity is assumed to vary as a linear function of temperature. A scaling group of transformations is applied to the governing equa- tions. The system remains invariant due to some relations among the transformation parameters. After finding three absolute invariants, a third-order ordinary differential equation corresponding to the momentum equation and two second-order ordinary differential equations corresponding to energy and diffusion equations are derived. The equations along with the boundary conditions are solved numerically. It is found that the decrease in the temperature-dependent fluid viscosity makes the velocity decrease with the increasing distance of the stretching sheet. At a particular point of the sheet, the fluid velocity decreases but the temperature increases with the decreasing viscosity. The impact of the thermophoresis particle deposition plays an important role in the concentration boundary layer. The obtained results are presented graphically and discussed.

Effects of temperature-dependent viscosity variation on entropy generation, heat and fluid flow through a porous-saturated duct of rectangular cross-section

Effect of temperature-dependent viscosity on fully developed forced convection in a duct of rectangular cross-section occupied by a fluid-saturated porous medium is investigated analytically. The Darcy flow model is applied and the viscosity-temperature relation is assumed to be an inverse-linear one. The case of uniform heat flux on the walls, i.e. the H boundary condition in the terminology of Kays and Crawford [12], is treated. For the case of a fluid whose viscosity decreases with temperature, it is found that the effect of the variation is to increase the Nusselt number for heated walls. Having found the velocity and the temperature distribution, the second law of thermodynamics is invoked to find the local and average entropy generation rate. Expressions for the entropy generation rate, the Bejan number, the heat transfer irreversibility, and the fluid flow irreversibility are presented in terms of the Brinkman number, the Péclet number, the viscosity variation number, the dimensionless wall heat flux, and the aspect ratio （width to height ratio）. These expressions let a parametric study of the problem based on which it is observed that the entropy generated due to flow in a duct of square cross-section is more than those of rectangular counterparts while increasing the aspect ratio decreases the entropy generation rate similar to what previously reported for the clear flow case by Ratts and Rant [14].

Mixed Convection of Non-Newtonian Erying Powell Fluid with Temperature-Dependent Viscosity over a Vertically Stretched Surface

The viscosity of a substance or material is intensely influenced by the temperature,especially in the field of lubricant engineering where the changeable temperature is well executed.In this paper,the problem of temperature-dependent viscosity on mixed convection flow of Eyring Powell fluid was studied together with Newtonian heating thermal boundary condition.The flow was assumed to move over a vertical stretching sheet.The model of the problem,which is in partial differential equations,was first transformed to ordinary differential equations using appropriate transformations.This approach was considered to reduce the complexity of the equations.Then,the transformed equations were solved using the Keller box method under the finite difference scheme approach.The validation process of the results was performed,and it was found to be in an excellent agreement.The results on the present computation are shown in tabular form and also graphical illustration.The major finding was observed where the skin friction and Nusselt number were boosted in the strong viscosity.

Analysis of Convective Transport of Temperature-Dependent Viscosity forNon-Newtonian Erying Powell Fluid: A Numerical Approach

Non-Newtonian is a type of fluid that does not comply with the viscosity under the Law of Newton and is being widely used in industrial applications.These include those related to chemical industries,cosmetics manufacturing,pharmaceutical field,food processing,as well as oil and gas activities.The inability of the conventional equations of Navier–Stokes to accurately depict rheological behavior for certain fluids led to an emergence study for non-Newtonian fluids’models.In line with this,a mathematical model of forced convective flow on non-Newtonian Eyring Powell fluid under temperature-dependent viscosity(TDV)circumstance is formulated.The fluid model is embedded with the Newtonian heating(NH)boundary condition as a heating circumstance and is assumed to move over a stretching sheet acting vertically.Using appropriate similarity variables,the respective model was converted into ordinary differential equations(ODE),which was later solved utilizing the Keller box approach.The present model is validated by comparing the existing output in literature at certain special limiting cases,where the validation results display a firm agreement.The current outputs for the proposed model are shown in tabular and graphical form for variation of skin friction plus Nusselt number,velocity and temperature distribution,respectively.

Advancements in Numerical Solutions:Fractal Runge-Kutta Approach to Model Time-Dependent MHD Newtonian Fluid with Rescaled Viscosity on Riga Plate

Fractal time-dependent issues in fluid dynamics provide a distinct difficulty in numerical analysis due to their complex characteristics,necessitating specialized computing techniques for precise and economical solutions.This study presents an innovative computational approach to tackle these difficulties.The main focus is applying the Fractal Runge-Kutta Method to model the time-dependent magnetohydrodynamic(MHD)Newtonian fluid with rescaled viscosity flow on Riga plates.An efficient computational scheme is proposed for handling fractal time-dependent problems in flow phenomena.The scheme is comprised of three stages and constructed using three different time levels.The stability of the scheme is shown by employing the Fourier series analysis to solve scalar problems.The scheme’s convergence is guaranteed for a time fractal partial differential equations system.The scheme is applied to the dimensionless fractal heat and mass transfer model of incompressible,unsteady,laminar,Newtonian fluid with rescaled viscosity flow over the flat and oscillatory Riga plates under the effects of space-and temperature-dependent heat sources.The first-order back differences discretize the continuity equation.The results show that skin friction local Nusselt number declines by raising the coefficient of the temperature-dependent term of heat source and Eckert number.The numerical simulations provide valuable insights into fluid dynamics,explicitly highlighting the influence of the temperature-dependent coefficient of the heat source and the Eckert number on skin friction and local Nusselt number.

Influences of clean fracturing fluid viscosity and horizontal in-situ stress difference on hydraulic fracture propagation and morphology in coal seam

The viscosity of fracturing fluid and in-situ stress difference are the two important factors that affect the hydraulic fracturing pressure and propagation morphology. In this study, raw coal was used to prepare coal samples for experiments, and clean fracturing fluid samples were prepared using CTAB surfactant. A series of hydraulic fracturing tests were conducted with an in-house developed triaxial hydraulic fracturing simulator and the fracturing process was monitored with an acoustic emission instrument to analyze the influences of fracturing fluid viscosity and horizontal in-situ stress difference on coal fracture propagation. The results show that the number of branched fractures decreased, the fracture pattern became simpler, the fractures width increased obviously, and the distribution of AE event points was concentrated with the increase of the fracturing fluid viscosity or the horizontal in-situ stress difference. The acoustic emission energy decreases with the increase of fracturing fluid viscosity and increases with the increase of horizontal in situ stress difference. The low viscosity clean fracturing fluid has strong elasticity and is easy to be compressed into the tip of fractures, resulting in complex fractures. The high viscosity clean fracturing fluids are the opposite. Our experimental results provide a reference and scientific basis for the design and optimization of field hydraulic fracturing parameters.

GLOBAL WELLPOSEDNESS OF MAGNETOHYDRODYNAMICS SYSTEM WITH TEMPERATURE-DEPENDENT VISCOSITY

The initial boundary value problem of the one-dimensional magneto-hydrodynamics system, when the viscosity, thermal conductivity, and magnetic diffusion coefficients are general smooth functions of temperature, is considered in this article. A unique global classical solution is shown to exist uniquely and converge to the constant state as the time tends to infinity under certain assumptions on the initial data and the adiabatic exponent γ. The initial data can be large if γ is sufficiently close to 1.

Laboratory study of fluid viscosity induced ultrasonic velocity dispersion in reservoir sandstones

Ultrasonic velocities of a set of saturated sandstone samples were measured at simulated in-situ pressures in the laboratory.The samples were obtained from the W formation of the WXS Depression and covered low to nearly high porosity and permeability ranges.The brine and four different density oils were used as pore fluids,which provided a good chance to investigate fluid viscosity-induced velocity dispersion.The analysis of experimental observations of velocity dispersion indicates that（1）the Biot model can explain most of the small discrepancy（about 2–3%）between ultrasonic measurements and zero frequency Gassmann predictions for high porosity and permeability samples saturated by all the fluids used in this experiment and is also valid for medium porosity and permeability samples saturated with low viscosity fluids（less than approximately 3 mP·S）and（2）the squirt flow mechanism dominates the low to medium porosity and permeability samples when fluid viscosity increases and produces large velocity dispersions as high as about 8%. The microfracture aspect ratios were also estimated for the reservoir sandstones and applied to calculate the characteristic frequency of the squirt flow model,above which the Gassmann’ s assumptions are violated and the measured high frequency velocities cannot be directly used for Gassmann’s fluid replacement at the exploration seismic frequency band for W formation sandstones.

Residence time distribution of high viscosity fluids falling film flow down outside of industrial-scale vertical wavy wall: Experimental investigation and CFD prediction

The flow behavior of gravity-driven falling film of non-conductive high viscosity polymer fluids on an industrial-scale vertical wavy wall was investigated in terms of film thickness and residence time distribution by numerical simulation and experiment.Falling film flow of high viscosity fluids was found to be steady on a vertical wavy wall in the presence of the large film thickness.The comparison between numerical simulation and experiment for the film thickness both in crest and trough of wavy wall showed good agreement.The simulation results of average residence time of falling film flow with different viscous fluids were also consistent with the experimental results.This work provides the initial insights of how to evaluate and optimize the falling film flow system of polymer fluid.

GLOBAL WELL-POSEDNESS OF THE 2D INCOMPRESSIBLE MICROPOLAR FLUID FLOWS WITH PARTIAL VISCOSITY AND ANGULAR VISCOSITY

This paper is concerned with the two-dimensional equations of incompress- ible micropolar fluid flows with mixed partial viscosity and angular viscosity. The global existence and uniqueness of smooth solution to the Cauchy problem is established.

Simulation of Variable Viscosity and Jeffrey Fluid Model for Blood Flow Through a Tapered Artery with a Stenosis

Non-Newtonian fluid model for blood flow through a tapered artery with a stenosis and variable viscosity by modeling blood as Jeffrey fluid has been studied in this paper. The Jeffrey fluid has two parameters, the relaxation time A1 and retardation time A2. The governing equations are simplified using the case of mild stenosis. Perturbation method is used to solve the resulting equations. The effects of non-Newtonian nature of blood on velocity profile, temperature profile, wall shear stress, shearing stress at the stenotsis throat and impedance of the artery are discussed. The results for Newtonian fluid are obtained as special case from this model.

Effect of Viscosity on Pumping-Up of Newtonian Fluid Driven by a Rotating Cone

Effect of viscosity on flow patterns of pumping-up of liquid generated by a cone rotating at the liquid surface has been experimentally studied with various concentrations of glycerol aqueous solution. We have previously found that the higher viscous non-Newtonian fluid was lifted-up along the conical surface with a radial filament-wise pattern, which is quite different from the monotonic thin film-wise pattern observed for the lower viscous fluid such as water. In order to elucidate the pumping-up mechanism, a transition diagram indicating the critical rotation rate is obtained as a function of viscosity?of Newtonian fluid in this study, varying from the lower value of water (μ?=?0.890 mPa·s) to the higher one of glycerin (μ?= 910?mPa·s). It is found that there are three categories depending on the viscosity classified as?1) film-wise pumping-up region for the viscosity?μ?≤?134?mPa·s,?2) filament-wise pumping-up one for the viscosity?μ?≥?520?mPa·s, and?3) no pumping-up phenomenon occurs?for 134??μ??mPa·s.

Jeffery-Hamel flow of non-Newtonian fluid with nonlinear viscosity and wall friction

A Jeffery-Hamel （J-H） flow model of the non-Newtonian fluid type inside a convergent wedge （inclined walls） with a wall friction is derived by a nonlinear ordinary differential equation with appropriate boundary conditions based on similarity relationships. Unlike the usual power law model, this paper develops nonlinear viscosity based only on a tangential coordinate function due to the radial geometry shape. Two kinds of solutions are developed, i.e., analytical and semi-analytical （numerical） solutions with suitable assumptions. As a result of the parametric examination, it has been found that the Newtonian normalized velocity gradually decreases with the tangential direction progress. Also, an increase in the friction coefficient leads to a decrease in the normalized Newtonian velocity profile values. However, an increase in the Reynolds number causes an increase in the normalized velocity function values. Additionally, for the small values of wedge semi-angle, the present solutions are in good agreement with the previous results in the literature.

Lie Group Analysis for the Effects of Variable Fluid Viscosity and Thermal Radiation on Free Convective Heat and Mass Transfer with Variable Stream Condition

Natural convective boundary layer flow and heat and mass transfer of a fluid with variable viscosity and thermal radiation over a vertical stretching surface in the presence of suction/injection is investigated by Lie group analysis. Fluid viscosity is assumed to vary as a linear function of temperature. The symmetry groups admitted by the corresponding boundary value problem are obtained by using a special form of Lie group transformations viz. scaling group of transformations. An exact solution is obtained for translation symmetry and numerical solutions for scaling symmetry. The effects of fluid viscosity and thermal radiation on the dimensionless velocity, temperature and concentration profiles are shown graphically. Comparisons with previously published works are performed and excellent agreement between the results is obtained. The conclusion is drawn that the flow field and temperature profiles are significantly influenced by these parameters.

Dynamic analysis of polymeric fluid in shear flow for dumbbell model with internal viscosity

The dynamic analysis of semi-flexible polymers,such as DNA molecules,is an important multiscale problem with a wide range of applications in science and bioengineering.In this contribution,a dumbbell model with internal viscosity was studied in steady shear flows of polymeric fluid.The tensors with moments other than second moment were approximated in the terms of second moment tensor.Then,the nonlinear algebraic equation of the second moment conformation tensor was calculated in closed form.Finally,substituting the resulting conformation tensor into the Kramers equation of Hookean spring force,the constitutive equations were obtained.The shear material properties were discussed for different internal viscosities and compared with the results of Brownian dynamics simulation.

BASIC EQUATIONS OF TURBULENT FLOW FOR VARIABLE DENSITY AND VARIABLE VISCOSITY NEWTONIAN FLUID IN OPEN CHANNEL

In this paper, using Navier-Stokes equations and Reynolds time-averaged rules, the turbulent motional differential equations of variable density and variable viscosity Newtonian fluid have been presented, and the turbulent motional differential equations of variable density and variable viscosity Newtonian fluid in open channel have been further proposed. The concepts of the density turbulence stress and the viscosity turbulence stress have been firstly presented in the paper.

EFFECT OF INTERNAL VISCOSITY OF POLYMERIC FLUIDS UNDER STRONG EXTENSIONAL FLOWS

The dumbbell model with internal viscosity for a dilute polymer solution is investigated based on a balance of viscous drag and restoring Brownian forces.An approximate method is used to obtain the solution of extensional stress in closed form in the case of steady flow.For different internal viscosities,this parametric study shows different asymptotic regimes of the extensional viscosity as a function of strain rate.This analysis may explain the attenuation of pressure drop in strong flows from a phenomeno...

STEADY-SHEAR VISCOSITY AND TRANSIENT STRESS RESPONSE FOR ELASTO-THIXOTROPIC FLUIDS

A phenomenological model for dispersed systems which exhibit complex theological behaviour such as shear and time-dependent viscosity, yield stress, and elasticity is proposed. The model extends the Quemeda model to describe the viscosity function with a structural parameter λ which varies according to differ- ent kinetic orders of particle aggregation and segregation. The transient stress response is obtained by solving an instantaneous Maxwell model with an assumed shear modulus function G of the same form as the viscosity function η. Accuracy of the proposed model is verified experimentally with the results obtained for two oil (creosote)/water emulsions. The model that gives the best fit of experimental data appears to be the one with kinetic orders n = m = 2.

Quantifying the Efficiency Advantages of High Viscosity Index Hydraulic Fluids

By providing higher in-use viscosity at elevated operating temperatures,hydraulic fluids with high viscosity index improve the efficiency of the hydraulic system.For mobile hydraulic equipment this efficiency can be quantified as an increase in fuel economy.This paper reviews the research that demonstrates these efficiency advantages in gear,vane and piston pumps and presents a method for predicting the overall fuel economy for a fleet of hydraulic equipment in operation.Finally a `Maximum Efficiency Hydraulic Fluid’ performance definition is presented which will enable an equipment operator to easily improve the performance of the system and reduce fuel consumption.

Experimental investigation of the effects of various parameters on viscosity reduction of heavy crude by oil-water emulsion

The effects of water content, shear rate, temperature, and solid particle concentration on viscosity reduction （VR） caused by forming stable emulsions were investigated using Omani heavy crude oil. The viscosity of the crude oil was initially measured with respect to shear rates at different temperatures from 20 to 70℃. The crude oil exhibited a shear thinning behavior at all the temperatures. The strongest shear thinning was observed at 20℃. A non-ionic water soluble surfactant （Triton X-100） was used to form and stabilize crude oil emulsions. The emulsification process has significantly reduced the crude oil viscosity. The degree of VR was found to increase with an increase in water content and reach its maximum value at 50 % water content. The phase inversion from oil- oil emulsion occurred at 30 in-water emulsion to water-in- % water content. The results indicated that the VR was inversely proportional to temperature and concentration of silica nanoparticles. For water-in-oil emulsions, VR increased with shear rate and eventually reached a plateau at a shear rate of around 350 s^-1. This was attributed to the thinning behavior of the continuous phase. The VR of oil-in-water emulsions remained almost constant as the shear rate increased due to the Newtonian behavior of water, the continuous phase.